Solve 2[7(2x-1)-3(4x-3)]-12=5[1-2(2-3x)]-19

$$2 [ 7 ( 2 x - 1 ) - 3 ( 4 x - 3 ) ] - 12 = 5 [ 1 - 2 ( 2 - 3 x ) ] - 19$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7 by 2x-1.

$$2\left(14x-7-3\left(4x-3\right)\right)-12=5\left(1-2\left(2-3x\right)\right)-19$$

Use the distributive property to multiply -3 by 4x-3.

$$2\left(14x-7-12x+9\right)-12=5\left(1-2\left(2-3x\right)\right)-19$$

Combine 14x and -12x to get 2x.

$$2\left(2x-7+9\right)-12=5\left(1-2\left(2-3x\right)\right)-19$$

Add -7 and 9 to get 2.

$$2\left(2x+2\right)-12=5\left(1-2\left(2-3x\right)\right)-19$$

Use the distributive property to multiply 2 by 2x+2.

$$4x+4-12=5\left(1-2\left(2-3x\right)\right)-19$$

Subtract 12 from 4 to get -8.

$$4x-8=5\left(1-2\left(2-3x\right)\right)-19$$

Use the distributive property to multiply -2 by 2-3x.

$$4x-8=5\left(1-4+6x\right)-19$$

Subtract 4 from 1 to get -3.

$$4x-8=5\left(-3+6x\right)-19$$

Use the distributive property to multiply 5 by -3+6x.

$$4x-8=-15+30x-19$$

Subtract 19 from -15 to get -34.

$$4x-8=-34+30x$$

Subtract 30x from both sides.

$$4x-8-30x=-34$$

Combine 4x and -30x to get -26x.

$$-26x-8=-34$$

Add 8 to both sides.

$$-26x=-34+8$$

Add -34 and 8 to get -26.

$$-26x=-26$$

Divide both sides by -26.

$$x=\frac{-26}{-26}$$

Divide -26 by -26 to get 1.

$$x=1$$